Nuprl Lemma : formal-sum-mul_wf
∀[S:Type]. ∀[K:CRng]. ∀[x:formal-sum(K;S)]. ∀[k:|K|]. (k * x ∈ formal-sum(K;S))
Proof
Definitions occuring in Statement :
formal-sum: formal-sum(K;S),
formal-sum-mul: k * x,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
crng: CRng,
rng_car: |r|
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
rng: Rng,
crng: CRng,
and: P ∧ Q,
quotient: x,y:A//B[x; y],
formal-sum: formal-sum(K;S),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
crng_wf,
formal-sum_wf,
rng_car_wf,
equal-wf-base,
formal-sum-mul_wf1,
bfs-equiv-rel,
bfs-equiv_wf,
basic-formal-sum_wf,
quotient-member-eq,
formal-sum-mul_functionality
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
universeEquality,
productEquality,
independent_functionElimination,
dependent_functionElimination,
independent_isectElimination,
lambdaEquality,
cumulativity,
hypothesis,
hypothesisEquality,
rename,
setElimination,
isectElimination,
extract_by_obid,
introduction,
thin,
productElimination,
pertypeElimination,
sqequalRule,
because_Cache,
pointwiseFunctionalityForEquality,
sqequalHypSubstitution,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[S:Type]. \mforall{}[K:CRng]. \mforall{}[x:formal-sum(K;S)]. \mforall{}[k:|K|]. (k * x \mmember{} formal-sum(K;S))
Date html generated:
2018_05_22-PM-09_45_42
Last ObjectModification:
2018_01_09-PM-06_08_49
Theory : linear!algebra
Home
Index